\documentclass[a4paper,12pt]{report}

\usepackage{amsthm,amssymb,amsmath}

\begin{document}

\begin{equation*}
f(t)=\left\{
 \begin{array}{rl}
  1 & \text{for} sin(2\pi\omega t)\ge 0 \\
   -1 & \text{for} sin(2\pi\omega t)\le 0 
 \end{array} \right
\end{equation*} 

\end{document}